Day 14 - Creating & Solving Inequalities from an Advance Context

BELL RINGER

Always do your best. What you plant

now, you will harvest later.

~Og Mandino

Draw

Bell Ringer

An inequality is like an equation, but

instead of an equal sign (=) it has one of

these signs:

< : less than

≤ : less than or equal to

> : greater than

≥ : greater than or equal to

≠ : not equal to

INEQUALITIES

Translations

Read Carefully!

5 more than x

x + 5

5 is more than x 5 > x

5 is less than x

5 < x

5 less than x

x - 5

5 less x

5 - x

The keyword(s) determine which math symbol to use

15

Creating Inequalities from Context

1. Read the problem statement first.
2. Reread the scenario and make a list or a table of the

known quantities.

3. Read the statement again, identifying the unknown

quantity or variable.

4. Create expressions and inequalities from the known

quantities and variable(s).

5. Solve the problem.
6. Interpret the solution of the inequality in terms of the

context of the problem.

Draw

Example Problems

Example 1
Alexis is saving to buy a laptop that costs $1,100. So far she
has saved $400. She makes $12 an hour babysitting. What’s
the least number of hours she needs to work in order to reach
her goal?

1. Read the problem statement first.

2. Reread the scenario and make a list or a table of

the known quantities.

Alexis has saved $400.
She makes $12 an hour.

She needs at least $1,100.

Example continued

3.

Read the statement again, identifying the unknown quantity
or variable.

You need to know the least number of hours Alexis must work to make

enough money. Solve for hours.

4.

Create expressions and inequalities from the known
quantities and variable(s).

Alexis’s saved money + her earned money must be greater than or equal

to the cost of the laptop.

400 + 12h ≥ 1100

20

Example, continued

5. Solve the problem.

400 + 12h ≥ 1100
Subtract 400 from both sides.

12h ≥ 700

Divide both sides by 12.

6.

Interpret the solution of the inequality in terms of the
context of the problem.

Therefore, Alexis needs to work at least 58.5 hours to make

enough money to save for her laptop.

Example 2
Juan has no more than $50 to spend at the mall. He wants to
buy a pair of jeans and some juice. If the sales tax on the jeans
is 4% and the juice with tax costs $2, what is the maximum price
of jeans Juan can afford?

1. Read the problem statement first.

2. Reread the scenario and make a list or a table of

the known quantities.

Sales tax is 4%.
Juice costs $2.

Juan has no more than $50.

Example continued

3. Read the statement again, identifying the unknown

quantity or variable.

The unknown quantity is the cost of the jeans.

4.

Create expressions and inequalities from the known
quantities and variable(s).

The price of the jeans + the tax on the jeans + the price of the juice

must be less than or equal to $50.

x + 0.04x + 2 ≤ 50

x + 0.04x + 2 ≤ 50

Add like terms.

1.04x + 2 ≤ 50

Subtract 2 from both sides.

1.04x ≤ 48

Divide both sides by 1.04.

x ≤ 46.153846

23

Example continued

5. Solve the problem.

x ≤ 46.16

6.

Interpret the solution of the inequality in terms of the
context of the problem.

Juan should look for jeans that are priced at or
below $46.16.

Example 3
A radio station is giving away concert tickets. There are 40
tickets to start. They give away 1 pair of tickets every hour
for a number of hours until they have at most 4 tickets left
for a grand prize. If the contest runs from 11:00 a.m. to 1:00
p.m. each day, for how many days will the contest last?

1.

Read the problem statement first.

2.

Reread the scenario and make a list or a table of the
known quantities.

The contest starts with 40 tickets.

The station gives away 2 tickets every hour.
The contest ends with at most 4 tickets left.

Example continued

3. Read the statement again, identifying the unknown

quantity or variable.

solve for hours (h)

4.

Create expressions and inequalities from the known
quantities and variable(s).

40 tickets – 2 tickets given away each hour must be less than or equal
to 4 tickets.

40 – 2h ≤ 4

Example continued

5. Solve the problem.
40 – 2h ≤ 4 Subtract 40 from both sides.
–2h ≤ –36 Divide both sides by –2 and

switch the inequality symbol.

h ≥ 18

6.

Interpret the solution of the inequality in terms of the
context of the problem.

number of days the contest

Multiple Choice

The room holds no more than 400 people. Which inequality represents the amount of people the room holds?

• P ≥ 400

• P ≤ 400

• P < 400

• P > 400

Multiple Choice

Steve runs more than 40 miles per week. Which inequality represents the amount of miles he runs?

• M < 40

• M ≥ 40

• M ≤ 40

• M > 40

Multiple Choice

Michael needs at least an 80% on his test. Which inequality represents the grade that Michael can get on his test?

• P ≥ 80
• P < 80
• P > 80
• P ≤ 80

Multiple Choice

Ms. Newkirk only has $20 to spend. Which inequality represents the amount which Ms. Newkirk can spend?

• M > 20
• M ≤ 20
• M < 20
• M ≥ 20

Multiple Choice

Sally needs 15 more votes to win. Which inequality represents the numbers of votes Sally needs?

• V < 15
• V > 15
• V ≥ 15
• V ≤ 15

Multiple Choice

The elevator holds a maximum of 700 pounds. Which inequality represents the amount of pounds the elevator can hold?

• P < 700
• P ≤ 700
• P > 700
• P ≥ 700

Multiple Choice

There must be no more than 10 people on the court. Which inequality describes the situation?

• x > 10
• x < 10
• x ⪯ 10
• x ⪰ 10

Multiple Choice

She needs at least 25 cupcakes for the party.  Which inequality describes the situation?

• x > 25
• x < 25
• x ⪯ 25
• x ⪰ 25

Multiple Choice

His age is less than his height. Which inequality describes the situation?

• a > h
• a < h
• a ⪯ h
• a ⪰ h

Multiple Choice

Which inequality represents the situation ten less than a number is no more than 30?

• 10 - x ⪯ 30
• x - 10 ⪯ 30
• 30 - x ⪯ 10
• x - 30 ⪯ 10

Multiple Choice

Which inequality represents the situation six more than twice a number is greater than 50?

• 6 + x > 50
• 6 + 2x < 50
• 2x + 6 > 50
• 6x + 2 > 50

Multiple Choice

Which inequality represents the following sentence: The ballroom has a capacity of 200 people.

• x > 200
• x < 200
• x ⪰ 200
• x ⪯ 200

Multiple Choice

Which inequality represents the following sentence: The dog costs at least $535.  

• x > 535
• x < 535
• x ⪰ 535
• x ⪯ 535

Multiple Choice

Jo has 8 friends and makes 2 new friends per week. She doesn't want any more than 16 friends. Create an inequality to determine the number of weeks it will take Jo to reach her desired number of friends.

• 2x + 8 ≤ 16
• 16x +8 < 2
• 8x +2 ≤ 16
• 2x + 16 < 8

Multiple Choice

Jim has $8 to spend on pizza. The slice is $4 and each topping is $0.50. Create an inequality to represent the number of toppings Jim can get if he only buys one slice of pizza.

• 4x + 0.50 ≥ 8
• .50x + 4 < 8
• 0.50x +4 ≤ 8
• 4x +0.50 ≤ 8

Multiple Choice

Your cell phone plan allows you 400 minutes to talk per month. So far this month, you have used 265 minutes and you have 7 days left on this month’s plan. Which inequality could you use to determine how many minutes at most you can use per day so that you don’t go over your monthly plan minutes?

• 7x + 265 < 400

• 7x + 265 ≤ 400

• 7x + 265 > 400

• 7x + 265 ≥ 400

Multiple Choice

Sydney has a $75 mall gift card. She wants to buy a sundress and a movie ticket. The movie ticket with tax costs $11.50. The sales tax on the sundress will be 4%. How much can the ticketed price of the sundress be?

• less than or equal to $61.06

• less than $61.06

• less than or equal to $45.36

• less than $45.36

Multiple Choice

A carafe at a banquet holds about 12 cups of coffee. When the carafe has 1 cup or less of coffee left, the waiter dumps the coffee out and pours in a fresh pot. Each coffee mug at the banquet holds 6 ounces of coffee. Assuming each person fills his or her mug, what inequality represents the number of people who can fill their mugs before the carafe needs to be refilled?

(Hint: 1 cup = 8 ounces)

• 12 – 0.75x ≤ 1

• 12 – x ≤ 1

• 12 – 0.75x ≥ 1

• 12 – x ≥ 1

Multiple Choice

Geraldine brings a large printing job to her local print shop. She doesn’t want to sit and wait for the job to completed, so she asks when she should come back to pick up her order. The machines print 30 pages per minute and 225 pages printed while she paid for her order. She has less than 1,000 pages left to go. How much longer will it take her order to print?

• more than about 33 minutes

• more than about 41 minutes

• less than about 33 minutes

• less than about 41 minutes

Multiple Choice

Juan is saving for a new computer and has saved $213. He is saving $3 a day and needs at least $654 for the computer he wants. How many weeks will it take him to save for the computer he wants?

• at most 147 weeks

• at most 21 weeks

• at least 147 weeks

• at least 21 weeks

Multiple Choice

A new grocery store is giving away four $20 gift certificates to the store every hour to celebrate its grand opening. The store manager wants to save at least 24 of the certificates to give to a local food bank. If there are 120 gift certificates to start with, for how many hours should the store continue giving them away?

• greater than or equal to 24 hours

• less than or equal to 24 hours

• less than 24 hours

• greater than 24 hours

Multiple Choice

When you graph an inequality, you used a closed dot when you use which symbols?

• ≤, ≥ 
• <, >

Multiple Choice

When graphing an inequality, you use an open dot when you use which symbol?

• <, >
• ≤, ≥ 

Multiple Choice

"At most" and "No more than" are both clue words for...

• <
• >
• ≤
• ≥

Multiple Choice

Write the phrase as an expression.
twice a number x plus 8 is greater than 12

• 2 + 8x < 12
• 2x + 8 > 12
• 2(x+8) ≠ 12
• 8(2+x) 

Multiple Choice

Does the given value make the inequality true? x + 9 > 21, when x = 15

• True

• Not True